To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Radius \( r = 12 \) feet
- Height \( h = \frac{1}{2} \times r = \frac{1}{2} \times 12 = 6 \) feet
Now substituting the radius and height into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (12^2) \times 6 \]
Calculating \( 12^2 \):
\[ 12^2 = 144 \]
Now substituting that back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 144 \times 6 \]
Calculating \( 144 \times 6 \):
\[ 144 \times 6 = 864 \]
Now substituting that in:
\[ V = \frac{1}{3} \times 3.14 \times 864 \]
Calculating \( 3.14 \times 864 \):
\[ 3.14 \times 864 = 2716.16 \]
Finally, dividing by 3:
\[ V = \frac{2716.16}{3} \approx 905.38666667 \]
Rounding to the nearest tenth:
\[ V \approx 905.4 \]
Thus, the volume of Erik’s cone is approximately 905.4 cubic feet.
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